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This article mainly investigates risk minimizing European currency option pricing and hedging strategy when the spot foreign exchange rate is driven by a Markov-modulated jumpdiffusion model. We suppose the domestic and foreign money market floating interest rates, the drift and the volatility of the exchange rate dynamics all depend on the state of the economy, which is modeled by a continuous-time hidden Markov chain. The model considered in this paper will provide market practitioners with flexibility in characterizing the dynamics of the spot foreign exchange rate. Using the minimal martingale measure, we obtain a system of coupled partialdifferential-integral equations satisfied by the currency option price and find the corresponding hedging strategies and the residual risk. According to simulation of currency option prices in the special case of double exponential jump diffusion regime switching model, we will further discuss and show the effects of the parameters on the prices.

The main influencing factors of the clustering effect of the k-means algorithm are the selection of the initial clustering center and the distance measurement between the sample points. The traditional k-mean algorithm uses Euclidean distance to measure the distance between sample points, thus it suffers from low differentiation of attributes between sample points and is prone to local optimal solutions. For this feature, this paper proposes an improved k-means algorithm based on evidence distance. Firstly, the attribute values of sample points are modelled as the basic probability assignment (BPA) of sample points. Then, the traditional Euclidean distance is replaced by the evidence distance for measuring the distance between sample points, and finally k-means clustering is carried out using UCI data. Experimental comparisons are made with the traditional k-means algorithm, the k-means algorithm based on the aggregation distance parameter, and the Gaussian mixture model. The experimental results show that the improved k-means algorithm based on evidence distance proposed in this paper has a better clustering effect and the convergence of the algorithm is also better.

Hepatocellular carcinoma (HCC) is a lethal malignancy with high mortality. The inhibition of cyclin-dependent kinase 7 (CDK7) activity has shown therapeutic efficacy in HCC. However, the underlying molecular mechanisms remain elusive. Here, we show that three HCC lines, HepG2, Hep3B, and SK-Hep-1, were highly susceptible to the CDK7 inhibitor THZ1. In mouse models, THZ1 effectively reduced HepG2 tumor growth and tumor weight. THZ1 arrested cell cycle and triggered MYC-related apoptosis in HepG2. To evaluate how MYC protein levels affected THZ1-induced apoptotic cell death, we overexpressed MYC in HepG2 and found that exogenously overexpressed MYC promoted cell cycle progression and increased cells in the S phase. THZ1 drastically engendered the apoptosis of MYC-overexpressing HepG2 cells in the S and G2/M phases. Importantly, transcription-inhibition-induced apoptosis is associated with DNA damage, and exogenous MYC expression further enhanced the THZ1-induced DNA damage response in MYC-overexpressing HepG2 cells. Consistently, in the HepG2 xenografts, THZ1 treatment was associated with DNA-damage-induced cell death. Together, our data indicate that the converged effect of MYC-promoted cell cycle progression and CDK7 inhibition by THZ1 confers the hypersensitivity of HCC to DNA-damage-induced cell death. Our findings may suggest a new therapeutic strategy of THZ1 against HCC.

Background Epidermal growth factor receptor (EGFR) overexpression is one of the most notable characteristics in head and neck squamous cell carcinoma (HNSCC). The MAPK kinase (MEK) inhibitor trametinib has shown efficacy to treat HNSCC; however, the molecular mechanism remains unclear. Methods HNSCC lines, mouse models, Western blot, and flow cytometry were employed to analyze the anticancer effects of trametinib. Results The JHU‐011, JHU‐022, and JHU‐029 HNSCC cells with different genetic alterations were highly susceptible to trametinib. Trametinib effectively reduced EGFR expression, which was accompanied by the reduction of pro‐survival protein MYC, and the increased expression of a MYC‐targeted cyclin‐dependent kinase inhibitor p27kip1 and pro‐apoptotic protein BIM. Trametinib resulted in G1 arrest of the cells, markedly reduced cell numbers in S phase, and significantly increased apoptosis. In mouse models, trametinib strongly inhibited tumors growth. Conclusions The MAPK–ERK signaling inhibition by trametinib may target EGFR and the downstream proteins against HNSCC.

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